Velocity obstacle

The velocity obstacle VOAB for a robot A, with position xA, induced by another robot B, with position xB and velocity vB.

In robotics and motion planning, a velocity obstacle, commonly abbreviated VO, is the set of all velocities of a robot that will result in a collision with another robot at some moment in time, assuming that the other robot maintains its current velocity.[1] If the robot chooses a velocity inside the velocity obstacle then the two robots will eventually collide, if it chooses a velocity outside the velocity obstacle, such a collision is guaranteed not to occur.[1]

This algorithm for robot collision avoidance has been repeatedly rediscovered and published under different names: in 1989 as a maneuvering-board approach,[2] in 1993 it was first introduced as the "velocity obstacle",[3] in 1998 as collision cones,[4] and in 2009 as forbidden velocity maps.[5] The same algorithm has been used in maritime port navigation since at least 1903.[6]

The velocity obstacle for a robot induced by a robot may be formally written as

where has position and radius, and has position , radius , and velocity . The notation represents a disc with center and radius .